Quantum and classical nonlinear dynamics in a microwave cavity

Charles H. Meaney, Hyunchul Nha, Timothy Duty, Gerard J. Milburn

Research output: Contribution to journalArticle

8 Citations (Scopus)


We consider a quarter wave coplanar microwave cavity terminated to ground via a superconducting quantum interference device. By modulating the flux through the loop, the cavity frequency is modulated. The flux is varied at twice the cavity frequency implementing a parametric driving of the cavity field. The cavity field also exhibits a large effective nonlinear susceptibility modelled as an effective Kerr nonlinearity, and is also driven by a detuned linear drive. We show that the semi-classical model corresponding to this system exhibits a fixed point bifurcation at a particular threshold of parametric pumping power. We show the quantum signature of this bifurcation in the dissipative quantum system. We further linearise about the below threshold classical steady state and consider it to act as a bifurcation amplifier, calculating gain and noise spectra for the corresponding small signal regime. Furthermore, we use a phase space technique to analytically solve for the exact quantum steady state. We use this solution to calculate the exact small signal gain of the amplifier.

Original languageEnglish
Article number7
JournalEPJ Quantum Technology
Issue number1
Publication statusPublished - 1 Dec 2014



  • Parametric amplifier
  • Quantum noise
  • Superconducting circuit

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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